I think of the possibility of former visitors from our world leaving behind some spy devices, if so, where could they be?
Our planet it is not a good place to hide an alien artifact, the Earth's surface, the sea and the atmosphere are in continuous motion with earthquakes, hurricanes and tsunamis. Nothing remains unchanged for a long time under the erosion caused by wind, or the corrosive action of oxygen.
The geological processes of erosion and sedimentation make impact craters disappear in a few millennia and Earth has received more impacts than the Moon.
Few places escape the activity of mountaineers, divers, geologists, paleontologists, drilling engineers or construction equipment.
Some shrines may remain unchanged for centuries, but they can also be destroyed by a rival religion, or by war.
A fixed facility can only monitor a small part of our civilization, but if it were on the visible face of the Moon it could scan the entire planet as it rotates.
It would also be exposed to meteorite impacts, as it lacks mobility it should be protected by a force field that could end up being detected by future technology.
It could be below the surface, with some sensors installed on the outside, but it would still be vulnerable to a lunar earthquake caused by a close impact.
Orbiting around Earth or the Moon the object could be detected by optical telescopes looking for exoplanets, by plugging the light of the stars in its path, or by colliding with remains of satellites.
Some position in space, named Lagrange Points, might constitute convenient parking places for automated alien probes.
The Earth-Sun gravitational system had five Lagrange Points, labelled L1 to L5, where the gravitational forces produced enhanced regions of attraction and repulsion that can be used by spacecraft to maintain its position without using any kind of propulsion.
The Earth-Moon system also had two Lagrange Points that have been investigated since 1956 by means of telescopes, infrared seekers, radar beams and two space probes, without finding anything but large concentration of cosmic dust.
The Earth-Sun points L1 and L2 have also been investigated by 17 space probes with the same results.
L4 and L5 are in the same orbit as Earth in fixed positions within a 60 degree arc ahead and behind the planet, are the most stable sites but they are too far away and have not yet been investigated.
L3 is always on the other side of the sun with respect to Earth and there is no point in looking there.
In my opinion, if there is an alien probe, it should orbit around the Sun and be equipped with a force field, to protect against micro-meteorites, a propulsion system to dodge the larger ones, long-range sensors based on undetectable technology for our radio telescopes and an FTL communication system to inform its base in real time, it would not make sense to use the radio to send messages hundreds of light years away, which could be detected by us.
If there is an FTL device out there it would be worth any effort to try to examine it, but it will be difficult to find it in the vastness that surrounds us.
There are three possible orbital configurations to look for: it could be in a very elongated elliptical orbit that allows you to visit the inner Solar System from time to time, as Comet Halley does, scan us for a few months to assess our evolution and return to deep space, it could be in a circular orbit within the inner Solar System and continuously evaluate us or in the outer Solar System approaching Earth only to study some interesting events, from an alien point of view.
They should be orbits perpendicular to the plane of the System to avoid impacts as much as possible. There are three regions relatively free of space objects: the area between the orbits of Venus and Earth, the one between Earth and Mars and the one between Saturn and Uranus.
Our most advanced optical systems can only locate objects larger than one kilometer but the object we should look for can be irregularly shaped, a size between a suitcase and a car, matt black surface, zero infrared emissions and stealth characteristics.
Perhaps the alien probe will discover its position when maneuvering to change orbit or to dodge an impact, or maybe we can detect the radiation emitted by its force field when it is hit by a rain meteorite as it crosses the trajectory of an ancient comet.
If we finally achieve reliable detection, it would be necessary to send a manned spaceship to investigate, but with the technology available, which does not even allow us to reach Mars, the journey could last for years.
We need to improve ionic propulsion, radiation protection and design some system that generates artificial gravity by rotation.
If all this were achieved, it must be noted that the alien probe detected the approach of our ship.
These four scenarios may occur: that you take an evasive action, initiate an attack, do nothing, or be scheduled to initiate a contact. Perhaps by demonstrating that we can locate her and go out to meet her, we will pass the test required by ET to enter the club of advanced civilizations.
In the third case I would have to try as aggressive a means of approach as possible, I think of a small robot with a transparent coating that says, 'I'm not hiding a gun.'
It should be parked halfway between the two ships issuing messages at all frequencies of the electromagnetic spectrum, except for the X-Rays frequency because it could be interpreted as an attack.
And then, waiting as long as it takes, we should not start a war that we cannot win by a misunderstanding, nor claim sovereignty over a Solar System that we cannot defend.
Only if after a reasonable time did the alien probe to continue without react would it be possible to insert it into the ship in order to study it.
It is doubtful that we could disassemble it without breaking something, possibly only a compact circuit integrated into a protective coating. A superior technology did not use screws, it could be limited to print-layering any artifact.
But the only sure thing about ET is that to get to us you will have used FTL technology and knowing that it is possible would also cause chaos among scientific stablishment. That might be a good reason why they don't officially announce their existence and just study us as we do with abyssal wildlife.
Bathyscape-UFO?